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P23 [Algebra] - Turkish NMO 1st Round - 2014

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May 26, 2014

Problem Statement

What is the minimum value of (x2+2x+8−43)⋅(x2−6x+16−43)(x^2+2x+8-4\sqrt{3})\cdot(x^2-6x+16-4\sqrt{3}) where xx is a real number?
<spanclass=′latex−bold′>(A)</span> 112−643<spanclass=′latex−bold′>(B)</span> 3−3<spanclass=′latex−bold′>(C)</span> 8−43<spanclass=′latex−bold′>(D)</span> 33−4<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 112-64\sqrt{3} \qquad<span class='latex-bold'>(B)</span>\ 3-\sqrt{3} \qquad<span class='latex-bold'>(C)</span>\ 8-4\sqrt{3} \\ <span class='latex-bold'>(D)</span>\ 3\sqrt{3}-4 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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